# Converting between Moles and Atoms

## By understanding the relationship between moles and Avogadro's number, we can convert between number of moles and number of atoms.

#### Key Points

• Avogadro's number is a very important relationship to remember: 1 Mole$6.022\times10^{23}$ atoms or molecules.

• To convert from moles to atoms, multiply the molar amount by Avogadro's number.

• To convert from atoms to moles, divide the atom amount by Avogadro's number (or multiply by its reciprocal).

#### Terms

• the number of atoms present in 0.012 kilograms of isotopically pure carbon-12, being 6.0221415 /times 10^{23}. By definition, the number of elementary entities (atoms or molecules) comprising one mole of a given substance

• In the International System of Units, the base unit of the amount of substance; the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kg of carbon-12. Symbol: mol. The number of atoms in a mole is known as Avogadro’s number.

#### Figures

1. ##### Converting Between Moles and Atoms

This conversion is easily facilitated by using Avogadro's number.

As introduced in the previous atom, the mole can be used to relate masses of substances to the quantity of atoms therein. The benefit thereof is an easy way of characterizing chemical reactions and determining how much of one substance can react with a given amount of another substance.

From moles of a substance, one can also find the number of atoms in a sample and vice versa. The bridge between atoms and moles is Avogadro's number, 6.022 x 1023.

Avogadro's number is dimensionless, but when it defines the mole, it can be expressed as 6.022 x 1023 mol-1; this form of the number is known as Avogadro's constant. This form shows the role of Avogadro's number as a conversion factor between the number of entities and the number of moles. Therefore, given the relationship 1 mol/6.022 x 1023 atoms, converting between moles and atoms of a substance becomes a simple dimensional analysis problem.

### Converting Moles to Atoms

Given a known number of moles (x), one can find the number of atoms in this molar quantity by multiplying it by Avogadro's number:

$x \ moles \cdot 6.02\cdot 10^{23} \frac{atoms}{1 \ mole} = y \ atoms$

For example, if we want to know how may atoms are in six moles of sodium, we could solve:

6 moles*(6.022*1023 atoms/mole)=3.61*1024 atoms

Note that the solution is independent of whether the element is sodium or otherwise.

### Converting Atoms to Moles

Reversing the calculation above, we can convert a number of atoms to a molar quantity by dividing it by Avogadro's number:

$\frac{x \ atoms}{6.022\cdot 10^{23} \frac{atoms}{1 \ mole}} = y \ moles$

This can be written without a fraction in the denominator by multiplying the number of atoms by the reciprocal of Avogadro's number:

$x \ atoms \cdot \frac{1 \ mole}{6.022\cdot 10^{23} \ atoms} = y \ moles$

For example, if we know there are 3.5*1024 atoms in a sample, we can calculate the number of moles this quantity represents:

3.5*1024 atoms*(1 mole/6.022*1023 atoms)=5.81 moles

#### Key Term Glossary

atom
the smallest possible amount of matter that still retains its identity as a chemical element, now known to consist of a nucleus surrounded by electrons
##### Appears in these related concepts:
chemical reaction
A process involving the breaking or making of interatomic bonds, in which one or more substances are changed into others.
##### Appears in these related concepts:
constant
Consistently recurring over time; persistent
##### Appears in these related concepts:
conversion factor
A conversion factor changes something to a different version or form.
##### Appears in these related concepts:
dimensional analysis
The study of the dimensions of physical quantities; used to obtain information about large complex systems, and as a means of checking mathematical and physics equations.
##### Appears in these related concepts:
dimensionless
of a physical constant, lacking units.
##### Appears in these related concepts:
element
Any one of the simplest chemical substances that cannot be decomposed in a chemical reaction or by any chemical means, and are made up of atoms all having the same number of protons.
##### Appears in these related concepts:
fraction
a part of a whole, especially a comparatively small part
##### Appears in these related concepts:
mass
The quantity of matter that a body contains, irrespective of its bulk or volume. It is one of four fundamental properties of matter. It is measured in kilograms in the SI system of measurement.
##### Appears in these related concepts:
mole
In the International System of Units, the base unit of the amount of substance; the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kg of carbon-12. Symbol: mol. The number of atoms in a mole is known as Avogadro’s number.
##### Appears in these related concepts:
solution
A homogeneous mixture, which may be liquid, gas or solid, formed by dissolving one or more substances.
##### Appears in these related concepts:
Solution
A homogeneous mixture, which may be liquid, gas or solid, formed by dissolving one or more substances.
##### Appears in these related concepts:
substance
Physical matter; material.